Table of Contents

Spring Semester

Timeframe	Content	Essential Questions	Skills	Resources	Assessment
Fall Semester Differential Calculus	Limits and continuity. Definition of the derivative Instantaneous rates of change Implicit differentiation Related rates Particle motion Graph theory Optimization	What does a limit and continuity have to do with differentiable functions? What is a derivative? What is its role? How can we apply the derivative in different real-world applications? How can we use the derivative to graph a function?	Calculate the limit of a function numerically,graphically and algebraically. Determine whether a function is continuous at a point or over an interval. Use the definition of the derivative in a proof. Compute the derivative of a function using the power rule, quotient rule, product rule, chain rule. Apply the derivative in related rates problems. Apply the first and second derivatives to graph a function. Apply the concept of the derivative in the context of velocity and acceleration of a particle moving in rectilinear motion.	Calculus. Concepts and Applications. Paul A. Foerster. The College Board website. www.apcentral.collegeboard.com Calculus. Graphical, Numerical, Algebraic. Finney, Demana, Waits and Kennedy D & S Marketing -- AP Calculus Multiple Choice and Free-Response Questions in Preparation for the AP Calculus (AB) Examination	Quizzes; Limit Bingo; Derivative Bingo; Tests; Multiple Choice questions from past AP exams; Free Response questions from past AP exams.
Spring Semester Integrable Calculus	Antiderivatives Slope fields Differential equations Fundamental Theorem of Calculus Definite integrals Area between curves Riemann Sums Trapezoidal Rule Accumulation Particle motion Graph theory Exponential growth & decay Volume of solids	What is an indefinite integral/antiderivative and how is it different from a derivative? What is a slope field? How do we solve variable-separable differential equations? What is the Fundamental Theorem of Calculus and how do we apply it? What is the difference between an indefinite integral and a definite integral? How do we use a Riemann Sum to find the area between two curves? What is the difference between actual area and net signed area? How can we use the notion of "accumulation" and the F.T.C.? How can we find the volume of solids of revolution? How can we use definite integrals in application of particle motion and exponential growth/decay? What is the relationship between the F.T.C. and graph theory?	Reversing the power rule and chain rule using different integration techniques--power rule, u-substitution, integration "by parts." Estimation of the definite integral using a finite Riemann Sum. Estimation of the definite integral using a Trapezoidal approximation. Properties of the Definite Integral. Calculate areas between curves using definite integrals. Calculate volumes of solids of revolution. Calculate volumes of solids of constant cross- sections. Understand a slope field as a graphical representation of a differential equation. Use a slope field to sketch a solution curve to a differential equation. Solve a differential equation algebraically. Sketch a function f(x) defined as a definite integral of a given function using the F.T.C.	Calculus: Concepts and Applications. Paul A. Foerster. The College Board website. www.apcentral.collegeboard.com Calculus. Graphical, Numerical, Algebraic. Finney, Demana, Waits and Kennedy D & S Marketing -- AP Calculus Multiple Choice and Free-Response Questions in Preparation for the AP Calculus (AB) Examination	quizzes; tests; Free Response and Multiple Choice questions from The College Board